Simply Complexity (4 page)

The objects can adapt their strategies according to their history.
This simply means that an agent can adapt its behavior by itself, in the hope of improving its performance.

The system is typically “open”.
This means that the system can be influenced by its environment, just like a market might be affected by outside news about the earnings of a particular company – or the traffic is affected by the closure of a particular road. By contrast, a closed system means one which is not in contact with the outside world – sort of like an office on a desert island with no Internet. And just like it sounds, such truly closed systems are rare. Much more common are systems that in some way are in contact with the outside world. In fact, the only truly closed system is the Universe as a whole. The trouble is, as we will see in
chapter 2
, that most fundamental theories in Physics only apply to closed systems. This is one reason why Complex Systems are so interesting not just to engineers, biologists and social scientists, but also to theoretical physicists.

The resulting system – a Complex System – will then show the following behaviors, all of which are characteristic of Complexity:

The system appears to be “alive”.
The system evolves in a highly non-trivial and often complicated way, driven by an ecology of agents who interact and adapt under the influence of
feedback. For example, financial analysts often talk as though the market were a living, breathing object, assigning it words such as pessimistic or bearish, and confident or bullish.

The system exhibits emergent phenomena which are generally surprising, and may be extreme.
In scientific terminology, the system is far from equilibrium. This basically means that anything can happen – and if you wait long enough, it generally will. For example, all markets will eventually show some kind of crash, and all traffic systems will eventually have some kind of jam. Such phenomena are generally unexpected in terms of when they arise – hence one aspect of surprise. But the system will also tend to exhibit emergent phenomena which are themselves surprising in that they could not have been predicted based on a knowledge of the properties of the individual objects. For example, no amount of understanding of the properties of water molecules could have led to the prediction that an iceberg would form and sink the
Titanic
as it passed. In terms of emergent phenomena such as market crashes and traffic jams, an important question concerns whether these extreme events might result from a sort of comedy of errors, like one domino knocking over another. For example, in the animated movie “Robots!” one small domino falling over eventually leads to a tidal wave of dominos – a sort of domino tsunami – upon which Mr. Bigwell and the other robots ended up surfing.

The emergent phenomena typically arise in the absence of any sort of “invisible hand” or central controller.
In other words, a Complex System can evolve in a complicated way all by itself. For this reason, Complex Systems are often regarded as being more than the sum of their parts which is just another way of saying “Two’s company, three is a crowd”. Given that the Universe itself is a Complex System of sorts, this feature deals a damaging blow to proponents of so-called Intelligent Design.

The system shows a complicated mix of ordered and disordered behavior.
For example, traffic jams arise at a particular point in time and at a particular place on a road network, and then later disappear. More generally, all Complex Systems seem to be able to move between order and disorder of their own accord. Put
another way, they seem to exhibit pockets of order. We return to this point later in the book.

But what is the value added by Complexity? After all, Complexity Science is only really of value if it can add new insights or lead to new discoveries – for example, by uncovering connections between phenomena which were previously considered unrelated. There is no point inventing a new name if we are just repackaging things that we already know. You might, for example, think that all the things that scientists traditionally look at are already sufficiently complicated to qualify as Complexity Science. As we shall see in later chapters, it is certainly true that many of the systems which scientists already study could be labelled as complex according to our list. However, the
way
in which scientists have traditionally looked at these systems does not use any of the insight of Complexity Science. In particular, the connections between such systems have not been properly explored – particularly between systems taken from different disciplines such as biology and sociology. Indeed it is fascinating to see if any insight gained from having partially understood one system, say from biology, can help us in a completely different discipline, say economics. One particular example of this is the ongoing research of Mark Fricker, Janet Efstathiou and Felix Reed-Tsochas at Oxford University, in which they analyze the nutrient supplylines in a fungus in order to see whether lessons can be learned for supply-chain design in the retail trade.

In an everyday context, the negative effect of overlooking similarities between supposedly unrelated systems, is akin to someone becoming an expert on the detailed cultural life of New York, Washington, and Boston – yet never realizing that these cities have a shared culture because of their location on the East Coast of the United States. Unfortunately such bridge-building is doubly difficult in a scientific context, because no individual scientist can possibly know the details of all the other research fields which might be relevant. This not only holds up the advance of Complexity
Science as a whole, but it also reduces the chances of new breakthroughs in our understanding of important real-world systems.

Much of traditional Physics has dealt with trying to understand the microscopic details within what we see. This has led to physicists smashing open atoms to look at the bits inside, and then smashing these bits open to see the bits inside the bits – eventually getting down to the level of quarks. It is certainly complicated – but this reductionist approach is in a sense the opposite of what Complexity is all about. Instead of smashing things apart to find out what the components are, Complexity focuses on what new phenomena can emerge from a collection of relatively simple components. In other words, Complexity looks at the complicated and surprising things which can emerge from the interaction of a collection of objects which themselves may be rather simple. Hence the philosophical questions driving Complexity Science are similar to those for the manufacturers of a toy like LEGO: starting with a set of quite simple objects, what can I make out of them, and what complicated and surprising things can I make them do? And what happens if I change one piece for another, does that change the types of things I can make? If I am missing a few pieces, or I add a few specialist pieces, how does that change the spectrum of possible things that can be built?

Going further, the underlying philosophy behind the search for a quantitative theory of Complexity is that we don’t need a full understanding of the constituent objects in order to understand what a collection of them might do. Simple bits interacting in a simple way may lead to a rich variety of realistic outcomes – and that is the essence of Complexity.

Complexity therefore represents a slap in the face for traditional reductionist approaches to understanding the world. For example, even a detailed knowledge of the specifications of a car’s engine, colour and shape, is useless when trying to predict where and when traffic jams will arise in a new road system. Likewise, understanding individuals’ personalities in a crowded bar would give little indication as to what large-scale brawls might develop. Within medical science, it is likely that no amount of understanding of an individual brain cell is likely to help us understand how to prevent or cure Alzheimer’s disease.

So what have we got so far? We have seen why Complexity is likely to be important not only for many areas of science, but also across many other disciplines and indeed everyday life. In particular, we have seen that its role in making connections between previously unrelated phenomena taken from distinct scientific disciplines is likely to be a very important one. For this reason, we can justifiably think of Complexity as a sort of umbrella science – or even, the Science of all Sciences.

One of the tell-tale characteristics that a particular system, such as traffic or a financial market, is complex is that it exhibits emergent phenomena which are surprising, extreme and self-generated – just think of a traffic jam or a financial market crash. Although it is certainly true that some traffic jams and market crashes are triggered by a particular outside event (for example, a road accident or the announcement of a particular company going bankrupt), more often than not there is no obvious reason either for their appearance or disappearance. In particular, they are not being engineered or controlled by some mysterious “invisible hand” operating in the background. So what makes them appear and disappear of their own accord?

We’ve all had the experience of driving happily along an apparently clear highway, only to suddenly find ourselves in a traffic jam for no apparent reason. And then, just as mysteriously, the jam disappears. We drive on, looking for an obvious cause for the jam such as an accident – but there is none. The same happens in financial markets, where it is actually quite rare that the cause of a given market crash can be assigned to a particular event or set of events. Indeed, for every financial expert who says that the cause of a given crash was X, you can find one who says it was Y. For example, the dot-com bubble which burst around April 2000 was supposedly “bound to happen”. But why did it happen at that specific time? And if these experts were so
certain that it would happen, why were they unable to predict it beforehand?

This remarkable ability of a Complex System to generate changes in its own behavior, means that a Complex System can appear to be jogging along quite happily in a fairly random way – and then all of a sudden it exhibits extreme behavior analogous to a traffic jam or market crash. There are many real-world systems which are sufficiently complex that they also show such extreme behavior; for example, cell-phone networks where the flow of data-packets plays the role of a flow of cars, and computer systems where the demand from users plays the role of the demand from traders. Even our own bodies are sufficiently complex that such extreme changes can arise; for example, a heart attack, an epileptic fit, a seizure, and a collapsed immune system, are all examples of a sudden, spontaneous and unexpected collective action within the body. Regardless of which of these phenomena we consider most relevant to our own lives, it is clearly very important to get to the bottom of what causes such extreme behavior – and then work out if we can predict it, control it, and possibly even avoid it.

But there is something very strange going on here. Phenomena like a traffic jam and a market crash are actually quite ordered effects, since they involve a collection of otherwise independent objects suddenly locking together in some fairly synchronized way. And yet they somehow emerge out of the everyday disorder of traffic and markets for no apparent reason – like a phoenix rising from the flames. For example, the appearance of a traffic jam means that a large number of cars that had previously been dotted all over the road in typical everyday traffic style, suddenly all become lined up in one single, slow-moving mass; and a market crash means that a financial market which had previously been filled with people buying and selling in apparently random fashion, suddenly becomes filled with people who have all decided to sell at the same time. What’s more, such effects can then disappear just as suddenly. So what is going on?

Complex Systems are able to move spontaneously back and forth between ordered behavior such as a traffic jam or a market
crash, and the disorder typical of everyday operation,
without any external help
. In other words, a Complex System can move freely between disorder and order, and back again, and can therefore be said to exhibit “pockets of order”. The emergence of such pockets of order has very important implications in terms of being able to predict and control the system. Their appearance is also quite mysterious – after all, if a bag of unsorted socks were a Complex System (which it isn’t) it should therefore be capable of organizing itself into an ordered pile of pairs, ready for placing in the clothes cupboard. A wonderful idea but as we all know it doesn’t happen in something as simple as a collection of socks. So there must be something more complicated going on at the heart of a Complex System which we need to understand. But the good news in practical terms is that pockets of order
can
indeed arise in a Complex System and this gives us hope that there might be a way of partially predicting the future evolution of such a system, and even being able to manage or control it.

These pockets of order can arise in both time and space. For example, traffic jams arise at a particular time and place, and then later disappear. Market crashes also arise at a particular time and in a particular world market, and then later disappear. The challenge in this chapter is to understand
why
such pockets of order arise. But to do this, we need to go on a journey from order to disorder – and where better to begin than a typical day at the office.

Why is it so hard to organize our desks? Or office? Or schedule? And why is it that after a few months’ use, even the most cared-for computer seems to run into all sorts of problems with file conflicts? The answer is simple: “disorder rules”.

Let’s look more closely at what this means. Take any set of organized objects, for example, the files in your office. Assuming you are very good at your job, these files will likely be arranged in a very specific way. Imagine that you have two files forming a pile on a shelf in your filing cabinet, and that you are
unfortunate enough to have been assigned a summer intern who is careless.